Branched block copolymers of butadiene and styrene are disclosed in U.S. Pat. No. 3,281,383 to Zelinski et al. These polymers have several advantageous properties. Further improvements were achieved by the so-called polymodal branched block copolymers of butadiene and styrene disclosed in U.S. Pat. No. 3,639,517 to Kitchen et al. The resins are described therein to have strength, clarity, processability and environmental durability. For many applications of these resins, their impact strength is an important feature. The impact strength is a measure of the impact the resin can stand without breaking. The higher the impact strength of a certain resin, the less likely it is that an article made from this resin will break when subjected to impacts or when dropped. It would, therefore, be desirable to increase the impact strength of said polymodal resins.